I'm not familiar with the "Knight's Tour."
However, to develop an object requires breaking down the system into in most rudimentary parts.
Suppose you were modelling a Chess game, you would first form an elementary (base) class, the ChessPiece, which has attributes of position. Then you would create new Classes for each Chess piece by inheriting the ChessPiece Class and adding new attributes and methods specific to the particular piece. For instance the Pawn can move either one or two positions only in the forward direction, therefore you would add a method for this movement including the above limitations. You would also need a method which described the "Taking of another Chess piece", etc.
BigDog